1. Field of the Invention
The present invention relates to a proximity effect correction method for improving dimensional accuracy of a developed pattern in preparation of exposure data for a charged particle beam exposure system.
2. Description of the Related Art
When a charged particle beam, for example an electron beam, is irradiated on a resist film on a substrate to draw a circuit pattern, there occurs such a phenomenon called forward scattering that a part of electrons of an incident electron beam scatters in the resist film prior to entry into the substrate, and such a phenomenon called backward scattering that electrons of the incident electron beam transmit the resist film and collide with nuclei of the substrate to scatter and come into the resist film again. Hence, an electron beam irradiated to one point on a resist film extends its influence on adjacent portions, producing a so-called proximity effect.
A basic exposure intensity distribution function f(X, Y) under the condition that an electron beam is irradiated to a point on a resist film of X=0 and Y=0, is approximately expressed by a following equation including forward and backward scattering terms of Gaussian functions.                               f          ⁡                      (                          X              ,              Y                        )                          =                              1                          π              ⁡                              (                                  1                  +                  η                                )                                              ⁢                      {                                                            1                                      β                    f                    2                                                  ⁢                                  exp                  ⁡                                      (                                          -                                                                                                    X                            2                                                    +                                                      Y                            2                                                                                                    β                          f                          2                                                                                      )                                                              +                                                η                                      β                    b                    2                                                  ⁢                                  exp                  ⁡                                      (                                          -                                                                                                    X                            2                                                    +                                                      Y                            2                                                                                                    β                          b                          2                                                                                      )                                                                        }                                              (        1        )            
where xcex7 is a ratio of a backscattering energy to a forward-scattering energy (hereinafter simply referred to as a xe2x80x9cbackscattering ratioxe2x80x9d), xcex2f is a forward-scattering radius and xcex2b is a backscattering radius. Values of the parameters are dependent on energy of an electron beam, a thickness of a resist film arid a material of the substrate, and are determined experimentally. With an acceleration voltage of an electron beam is higher, xcex2f is smaller while xcex2b is larger.
In a prior art proximity effect correction method, an exposure dose was determined in such a way that evaluation points are set at middle points of edges or corners of a pattern to be exposed, an exposure intensity at each evaluation point is calculated with the equation (1), and an exposure dose distribution is determined in such a way that the square-sum of the differences between the exposure intensities and a target value is minimized.
However, in company with progress toward higher integration of Large Scale Integration (LSI), the number of figures of a pattern has rapidly increased, making a calculation time excessively long.
Therefore, such a proximity effect correction method has been desired that it is possible to reduce a calculation time and to limit a dimensional error of a developed pattern within an allowable range.
As one of such methods, for example, JP 2502418 and Journal of Vacuum Science Technology, Vol. B10, No. 6, pp. 3072-3076 disclose a method of approximately calculating backscattering exposure intensity at the mesh of interest, comprising the steps of partitioning a placement surface of an LSI pattern to be exposed into rectangular meshes, calculating pattern area densities in the respective meshes, and taking an influence coming from surroundings meshes to the mesh of interest into consideration based on the backscattering term of the equation (1). Using this method, an exposure dose is determined in such a way that a sum of a half of a peak value of a forward-scattering exposure intensity distribution and a backscattering exposure intensity is constant.
According to this method, dimensional variations in a developed pattern in a wide area, caused by an influence of backscattering, can be prevented with a simple algorithm.
However, this method has the following problems.
(1) Since the expanse of the deposited energy distribution due to forward scattering is not taken into consideration, there is no assurance that dimensions of a developed pattern coincide with those in design. That is, since with a pattern is finer, the expanse of the deposited energy distribution near a half of a peak value thereof is not negligible, a developed pattern is fatter than its design pattern.
(2) In a region where a pattern area density changes rapidly and a dimensional variation of a pattern within one shot becomes conspicuous, as,kin a peripheral region of a DRAM cell array, correction is insufficient.
In order to solve the problem (1), a Japanese Patent Application of Publication No. 11-26360 discloses a method that performs a proximity effect correction using a pattern area density after offsetting a dimension L of an exposure pattern by a predetermined value xcex94L. In this method, in order to improve a latitude, after a design pattern is previously applied with a dimensional offset of xcex94L, the equation of exposure intensity distribution is transformed into a form including the offset size when performing a proximity effect correction by means of a pattern area density method, whereby a change in pattern area density caused by the size offset is taken into consideration.
In this method, however, since there is disclosed no definite value xcex94L of the size offset to be different depending on a pattern size but a general, technical concept is simply shown, therefore there is no guarantee that dimensions of a developed pattern coincide with those in design in an actual electron beam exposure.
In order to solve the problem (2), there is disclosed, in a Japanese Patent Application of Publication No. 8-31727, an invention in which one shot size (a size of pattern partitioning) is made smaller only in a region where a pattern area density changes rapidly and thereby, a dimensional accuracy is improved in such a region. For example, a stencil mask is employed, and each of block patterns is exposed with one shot in the middle region of a memory cell array where an influence of backscattering from its surroundings is almost constant, while a variable-shaped rectangular exposure of a small size is performed in the peripheral region of the memory cell array.
However, since the number of shots per a unit area in the peripheral region of the,memory cell array increases, a though put decreases. If block patterns of a small size are formed on the stencil mask in order to expose the peripheral region in blocks, the number of block patterns to be formed in a limited space on the mask increase, thereby increasing patterns that cannot be exposed in blocks to reduce a throughput.
A Japanese Patent No. 2,842737 discloses such a method that exposure in a region where a pattern area density changes rapidly is superimposed by an auxiliary shot whose focus is out (changed from the best so that beam profile is blurred, thereby improving dimensional accuracy of a developed pattern. In this method, an auxiliary exposure whose focus is out is applied to a peripheral region where an actual exposure intensity becomes short when in adoption of an exposure intensity calculated based on a pattern area density method in a middle portion of a device pattern, thereby making exposure intensity in the middle portion equal to that in the peripheral region.
However, since out-of-focus beam size is almost equal to a backscattering radius xcex2b, the out-of-focus amount increases as an acceleration voltage of an electron beam becomes higher and application of this method becomes hard. For example, if an acceleration voltage is 50 kV, then xcex2f=0.028 xcexcm and xcex2b=11.43 xcexcm. Further, since a mesh size in a pattern area density calculation is about a backscattering radius xcex2b and correction is Effected in units of a mesh, with an acceleration voltage increases, dimensional accuracy of a developed pattern is degraded. In addition to this, since there is a need to change a beam focal point in large amount to get out of focus required while exposing, this is a cause for reducing throughput.
Accordingly, it is an object of the present invention to provide a charged particle beam exposure method using a proximity effect correction method by which dimensional accuracy of a developed pattern is improved without a great increase in calculation times
It is another object of the present invention to provide a charged particle beam exposure method using a proximity effect correction method by which the number of shots per a unit area can be decreased with simple data processing without reducing dimensional accuracy of a developed pattern in a region where effective pattern area densities change rapidly.
According to the first aspect of the present invention, there is provided a charged particle beam exposure method with performing proximity effect correction comprising: a self-correction step of adjusting a design width in such a way that a peak width, which is a width of an exposure intensity distribution at a height of a predetermined percent of a peak value thereof, is equal to the design width, the distribution being obtained by calculating a surface integral of a forward-scattering term of a basic exposure intensity distribution function over a pattern of interest; and an exposure dose correction step of determining a corrected exposure dose Qcp in such a way that a product of the corrected exposure dose Qcp and a sum of first and second values is substantially constant, where the first value is equal to the predetermined percent of the peak value and the second value is equal to an exposure intensity due to a backscattering term of the basic exposure intensity distribution function.
With the first aspect, since a self-correction step of changing a design width in consideration of a forward-scattering term is executed prior to an exposure dose correction step, and in the exposure dose correction step, a backscattering term is further considered on a result obtained in consideration of the forward-scattering term, therefore dimensions of a developed pattern can be those of design with good accuracy.
Further, since it is enough to consider only a single pattern of interest in the self-correction step, a great increase in calculation time can be suppressed.
If a half-width is adopted as a peak width, a change in dimension of a developed pattern due to an error in exposure dose is small since a gradient of the exposure intensity distribution at the height of a half of a peak value is roughly larger than at other positions.
If the exposure dose correction step is executed using a pattern area density method, calculation becomes comparatively easy.
According to the second aspect of the present invention, there is provided a charged particle beam exposure method with performing proximity effect correction comprising: partitioning a placement surface of an exposure pattern into meshes each smaller in area than a maximum size of one shot for pattern expo sure; determining a pattern area density of each mesh; determining an effective pattern area density by smoothing the pattern area densities; determining an exposure intensity due to a backscattering term of a basic exposure intensity distribution function as a value proportional to the effective pattern area density; and performing auxiliary exposure on meshes each short of an exposure dose with one shot for a pattern.
With the second aspect since an auxiliary exposure shot for the meshes each smaller in area than a maximum size of one shot for pattern exposure are superimposed on a pattern exposure shot in simple data processing, the number of shots in a unit area can be decreased compared to a case of variable-shaped rectangular exposure without reducing dimensional accuracy in a developed pattern in a region where pattern area densities change rapidly.